-4w^2-23w-33=0

Solution for -4w^2-23w-33=0 equation:

Simplifying
-4w2 + -23w + -33 = 0

Reorder the terms:
-33 + -23w + -4w2 = 0

Solving
-33 + -23w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(33 + 23w + 4w2) = 0

Factor a trinomial.
-1((3 + w)(11 + 4w)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
Subproblem 2
Set the factor '(11 + 4w)' equal to zero and attempt to solve:

Simplifying
11 + 4w = 0

Solving
11 + 4w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + 4w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 4w = 0 + -11
4w = 0 + -11

Combine like terms: 0 + -11 = -11
4w = -11

Divide each side by '4'.
w = -2.75

Simplifying
w = -2.75
Solution
w = {-3, -2.75}